Question

Farrell and colleague measured the effect of oxygen deprivation on the motor behaviour of rats on how long they can stay hanging in a bar. Their results showed a mean of m = 76 seconds and a standard deviation of s = 12 seconds.

a) What is the semi-interquartile range value?

b) What is the value for the first quartile?

Answer 1

Solution:-

Given that,

mean = = 76

standard deviation = = 12

Using standard normal table,

The z dist'n First quartile is,

P(Z < z) = 25%

= P(Z < z) = 0.25  

= P(Z < -0.6745 ) = 0.25

z = -0.6745

Using z-score formula,

x = z * +

x = -0.67 * 12 +76

x = 67.96

First quartile =Q1 = 67.96

The z dist'n Third quartile is,

P(Z < z) = 75%

= P(Z < z) = 0.75  

= P(Z < 0.6745 ) = 0.75

z = 0.6745

Using z-score formula,

x = z * +

x = 0.67 * 12 +76

x = 84.04

Third quartile =Q3 = 84.04

IQR = Q3 - Q1

= 84.04 - 67.96

= 16.08

The semi-interquartile range value = 16.08